A Bayesian computational technique for learning the airflow resistance of acoustical fibrous materials at high temperatures

This study investigates the acoustic performance of various porous materials at elevated temperatures, employing Constrained Gaussian Process Regression (CGPR) to model the relationship between specific airflow resistance and the absolute temperature. Experimental data on six fibrous material samples at 600°C are used to develop and compare CGPR models against conventional Power Law Regression (PLR) methods. The developed CGPR incorporates constraints such as boundedness, monotonicity and convexity/concavity derived from the evident relationships and prior knowledge of the specific airflow resistance versus temperature variations. The results of this study prove the outperformance of the developed CGPR over PLR methods in terms of data efficiency, predictive accuracy, uncertainty quantification, overfitting recovery and extrapolation capability. This comparative analysis outlines a significant improvement in the predictive accuracy of CGPR, achieving improved coefficient of determination values compared to PLR. CGPR also furnishes a direct strategy to quantify the uncertainty of predictions which is vital for applications at elevated temperatures. Additionally, CGPR offers valuable insights into sound absorption behaviour, highlighting its applicability in thermal acoustics and materials engineering. Prospective research avenues stem from this research as the developed CGPR technique has the potential to replace various modelling techniques in materials science and acoustic engineering applications.